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ΓL(1,𝔽8)×C11⋊Dic11 #23778992

order10164
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C11

Aliases

direct productΓL(1,𝔽8)×C11⋊Dic11
unambiguous semidirect productC11⋊(ΓL(1,𝔽8)×Dic11)

Splittings

derived, HallC7×C112 ⋊ C3×C4
HallC7×C11⋊Dic11 ⋊ C3
HallC112×ΓL(1,𝔽8) ⋊ C4
SylowC112 ⋊ C4×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C11⋊Dic11

Subgroups

subgroupG/H
center, Frattini, hypercenterC2ΓL(1,𝔽8)×C11⋊D11
commutator, hypocenterC7×C112C3×C4
Fitting, socle, cosocleC2×C7×C112C2×C3
prime radicalC2×C112×ΓL(1,𝔽8)C2
LCSG ▷ C7×C112
UCSC1 ◁ C2

168 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

620 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)×(C11⋊Dic11)⋊C3, C3×ΓL(1,𝔽8)×C11⋊Dic11, ΓL(1,𝔽8)×C3⋊(C11⋊Dic11)
maximal normal subgroup ofΓL(1,𝔽8)×(C11⋊Dic11)⋊C3, C3×ΓL(1,𝔽8)×C11⋊Dic11
maximal quotient ofC7⋊C9×C11⋊Dic11, C3×ΓL(1,𝔽8)×C11⋊Dic11, ΓL(1,𝔽8)×C3⋊(C11⋊Dic11)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10164, 44);